Beyond the extended Selberg class: $1
Year: 2020
Type: preprint
Abstract: We show that a class of Dirichlet series ${\mathfrak{A}}^{\#}$ that is much larger than the extended Selberg class ${\mathscr{S}}^{\#}$, and also contains the standard as well as the tensor product, exterior square and symmetric square $L$-functions of automorphic $L$-functions of $GL_n$ over number fields, does not have any elements of degrees between $1$ and $2$. The proof of our more general theorem is very different from the proof of Kaczorowski and Perelli for the class ${\mathscr{S}}^{\#}$, and is much shorter and simpler even in that case.
Source: arXiv (Cornell University)
Authors: Balasubramanian, R., Raghunathan, Ravi
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394655361